APPENDIX TO CHAPTER XIII 389

on January 1 and half on July 1, six months later, and that,
as before, each element of the stock remains one year before

sale. The cost on January 1 is 3 and on July 1 is also 3

If we take inventory on July 1, the stock just purchased represents

 a value , while that purchased six months before, and

V4

which is to be disposed of in six months more, may be taken

as having a somewhat greater value, namely, oY 1+, the

latter being the cost value plus interest, or, what amounts to
the same thing, the expected selling value less interest. The
total stock is therefore worth on July 1, —

ru Oh bude cts
ot 2 V1 -+ 2.
The sales or receipts from the stock will evidently be every six
months 5 (1471), this being the accumulated value for one

year of the amount purchased, z. For the entire year the

receipts will thus be just double, or ¢ (1 +¢). If from this
we deduct the per annum cost, ¢, we obtain, as before, the
net income, ¢i. The ratio of this net income to the capitalvalue
 taken on January 1 or July 1, of any year, will therefore
be, —
ci
stsviTi
2
1+ vii
seems no longer to be equal to the rate of interest; but the discrepancy
 is due to the fact that the merchant’s income accrues

semi-annually, whereas i is reckoned annually. If we substitute
 for i its value in terms of i/, the rate of interest reckoned

This expression, which is evidently the same as

3'2 . .
semi-annually (namely, ¢'+ : , as shown in the Appendix to

Chap. XII, § 2), we shall find, on simplifying, that the above
expression reduces to i. In other words, in the artificially
simple case in which the merchant is supposed to accomplish